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AP Calculus AB. Day 12 Section 2.6. 1. The base of a 25-foot ladder is being pulled away from the house it leans on at a rate of 4 feet per second. At what rate is the top of the ladder moving when the base of the ladder is 7 feet from the building?. 25. y. x. 25. 24. 7. - PowerPoint PPT Presentation
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04/21/23 Perkins
AP Calculus AB
Day 12Section 2.6
ftsec4
dx
dt
1. The base of a 25-foot ladder is being pulled away from the house it leans on at a rate of 4 feet per second. At what rate is the top of the ladder moving when the base of the ladder is 7 feet from the building?
Find .dy
dt7 feetx
x
y2 2 25x y
7
24
25
25
2 2 0dx dyx ydt dt
2 7 4 2 0dy
ydt
2 7 4 2 24 0dy
dt
56
48
dy
dt
sec
7
6ft
sec4 ftdx
dt
2a. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which his shadow’s length is changing when he is 10 feet from the base of the light.
13
6
d
s
10 ftx
Find .ds
dt
13 6s d
sx
d
6
13 ft
d x s
13 6 6s x s 7 6s x
7 6ds dx
dt dt
7 6 4ds
dt
sec
24
7ft
ds
dt
sec4 ftdx
dt
2b. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which the position of the tip of his shadow is changing when he is 10 feet from the base of the light.
10 ftx
Find .dd
dt
d x s
sec
24
7ft
ds
dt
dd dx ds
dt dt dt
244
7 sec
52
7ft
sx
d
6
13 ft
ftsec1
dr
dt
3. A fishing line is reeled in at a rate of 1 foot per second from a bridge that is 15 feet above the water. At what rate is the angle between the line and the water changing when 25 feet of line is out?
Find .d
dt
25 feetr
x
15
15sin
r
20
15
r
115r
2cos 15d dr
rdt dt
25
2
20 151
25 25
d
dt
2
15 25
2025
d
dt
sec
3
100rad
Perkins
AP Calculus AB
Day 12Section 2.6
1. The base of a 25-foot ladder is being pulled away from the house it leans on at a rate of 4 feet per second. At what rate is the top of the ladder moving when the base of the ladder is 7 feet from the building?
2a. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which his shadow’s length is changing when he is 10 feet from the base of the light.
2b. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which the position of the tip of his shadow is changing when he is 10 feet from the base of the light.
3. A fishing line is reeled in at a rate of 1 foot per second from a bridge that is 15 feet above the water. At what rate is the angle between the line and the water changing when 25 feet of line is out?
